During a Mathematics class, the teacher suggests to the students that a Cartesian coordinate system $(x, y)$ be established and represents on the board the description of five algebraic sets, I, II, III, IV and V, as follows:
I - is the circle with equation $x^{2} + y^{2} = 9$; II - is the parabola with equation $y = -x^{2} - 1$, with $x$ varying from $-1$ to $1$; III - is the square formed by the vertices $(-2,1)$, $(-1,1)$, $(-1,2)$ and $(-2,2)$; IV - is the square formed by the vertices $(1,1)$, $(2,1)$, $(2,2)$ and $(1,2)$; V - is the point $(0,0)$.
Next, the teacher correctly represents the five sets on the same grid, composed of squares with sides measuring one unit of length each, obtaining a figure.
Which of these figures was drawn by the teacher?
(A), (B), (C), (D), (E) [as shown in the figures]

A pharmaceutical company conducted a study of the efficacy (in percentage) of a medication over 12 hours of treatment in a patient. The medication was administered in two doses, with a 6-hour interval between them. As soon as the first dose was administered, the medication's efficacy increased linearly for 1 hour, until reaching maximum efficacy (100\%), and remained at maximum efficacy for 2 hours. After these 2 hours at maximum efficacy, it began to decrease linearly, reaching 20\% efficacy upon completing the initial 6 hours of analysis. At this moment, the second dose was administered, which began to increase linearly, reaching maximum efficacy after 0.5 hours and remaining at 100\% for 3.5 hours. In the remaining hours of analysis, the efficacy decreased linearly, reaching 50\% efficacy at the end of treatment.
Considering the quantities time (in hours) on the horizontal axis and medication efficacy (in percentage) on the vertical axis, which graph represents this study?
(A), (B), (C), (D), (E) [see figures]

11. As shown in the figure, the rectangle's edge, is the midpoint, point moves along the edge, and moves with, denote, express the sum of distances from the moving point to two points as a function of, then the graph of is approximately
[Figure]
A.
[Figure]
B.
[Figure]
C.
[Figure]
D.

As shown in the figure, rectangle $ABCD$ has sides $\mathrm { AB } = 2 , \mathrm { BC } = 1$, and $O$ is the midpoint of $AB$. Point $P$ moves along edges $\mathrm { BC } , \mathrm { CD }$, and $DA$, with $\angle \mathrm { BOP } = \mathrm { x }$. The sum of distances from moving point $P$ to points $A$ and $B$ is expressed as a function of $x$, denoted $f ( x )$. The graph of $f ( x )$ is approximately
(A), (B), (C), or (D) [as shown in figures]

The graph of the function $y = 2 x ^ { 2 } - e ^ { | x | }$ on $[ - 2,2 ]$ is approximately
(A), (B), (C), (D) [as shown in the figures]

The graph of the function $f ( x ) = \frac { \mathrm { e } ^ { x } - \mathrm { e } ^ { - x } } { x ^ { 2 } }$ is approximately (see options A, B, C, D in the figures).

The graph of function $f ( x ) = \frac { \mathrm { e } ^ { x } - \mathrm { e } ^ { - x } } { x ^ { 2 } }$ is approximately
A. [Graph A]
B. [Graph B]
C. [Graph C]
D. [Graph D]

The graph of the function $y = - x ^ { 4 } + x ^ { 2 } + 2$ is approximately (See figures A, B, C, D in the original paper.)

The graph of the function $y = \frac { 2 x ^ { 3 } } { 2 ^ { x } + 2 ^ { - x } }$ on $[ - 6,6 ]$ is approximately
A. [graph A]
B. [graph B]
C. [graph C]
D. [graph D]

5. The graph of function $f ( x ) = \frac { \sin x + x } { \cos x + x ^ { 2 } }$ on $[ - \pi , \pi ]$ is approximately
A. [Figure]
B. [Figure]
C. [Figure]
D. [Figure]

7. The graph of the function $y = \frac { 2 x ^ { 3 } } { 2 ^ { x } + 2 ^ { - x } }$ on $[ - 6,6 ]$ is approximately
A. [Figure]
B. [Figure]
C. [Figure]
D. [Figure]

The graph of the function $f ( x ) = \left( 3 ^ { x } - 3 ^ { - x } \right) \cos x$ on the interval $\left[ - \frac { \pi } { 2 } , \frac { \pi } { 2 } \right]$ is approximately [see figures A, B, C, D in the original paper].

The graph of the function $y = \left( 3 ^ { x } - 3 ^ { - x } \right) \cos x$ on the interval $\left[ - \frac { \pi } { 2 } , \frac { \pi } { 2 } \right]$ is approximately: (see figures A, B, C, D)

The figure on the right is the approximate graph of one of the following four functions on the interval $[ - 3,3 ]$ . The function is
A. $y = \frac { - x ^ { 3 } + 3 x } { x ^ { 2 } + 1 }$
B. $y = \frac { x ^ { 3 } - x } { x ^ { 2 } + 1 }$
C. $y = \frac { 2 x \cos x } { x ^ { 2 } + 1 }$
D. $y = \frac { 2 \sin x } { x ^ { 2 } + 1 }$

The equation $x ^ { 3 } + y ^ { 3 } = x y ( 1 + x y )$ represents
(a) Two parabolas intersecting at two points
(b) Two parabolas touching at one point
(c) Two non-intersecting hyperbolas
(d) One parabola passing through the origin.

For a real polynomial in one variable $P$, let $Z ( P )$ denote the locus of points ( $x , y$ ) in the plane such that $P ( x ) + P ( y ) = 0$. Then,
(A) there exist polynomials $Q _ { 1 }$ and $Q _ { 2 }$ such that $Z \left( Q _ { 1 } \right)$ is a circle and $Z \left( Q _ { 2 } \right)$ is a parabola.
(B) there does not exist any polynomial $Q$ such that $Z ( Q )$ is a circle or a parabola.
(C) there exists a polynomial $Q$ such that $Z ( Q )$ is a circle but there does not exist any polynomial $P$ such that $Z ( P )$ is a parabola.
(D) there exists a polynomial $Q$ such that $Z ( Q )$ is a parabola but there does not exist any polynomial $P$ such that $Z ( P )$ is a circle.

A water pumping station found that its electricity consumption (unit: kilowatt-hours) is directly proportional to the cube of the pump motor speed (unit: rpm). Based on this, which of the following five graphs best describes the relationship between the electricity consumption $y$ (kilowatt-hours) and the pump motor speed $X$ (rpm) of this water pumping station?
(1) [Graph 1] (2) [Graph 2] (3) [Graph 3] (4) [Graph 4] (5) [Graph 5]

Let $a, b, c$ and $d$ be real numbers such that
$$x + ay \leq b$$ $$x + cy \geq d$$
The solution set of the system of inequalities is shown in green on the coordinate plane below.
Accordingly, what are the signs of the numbers $a, b, c$ and $d$ in order?
A) $+, -, -, -$ B) $+, +, +, -$ C) $+, -, +, -$

For real numbers $\mathrm{a}$, $\mathrm{b}$ and $\mathrm{c}$ with $\mathrm{a} \cdot \mathrm{b} \cdot \mathrm{c} > 0$, a function $f$ is defined on the set of real numbers as
$$f(x) = ax^{2} + bx + c$$
Accordingly, the graph of function $f$ can be which of the graphs shown (I, II, III)?
A) Only I B) Only II C) I and III D) II and III E) I, II and III